Abstract

A dynamic model for metabolic reaction network of Penicillium chrysogenum, coupling the central metabolism to growth, product formation and storage pathways is presented. In constructing the model, we started from an existing stoichiometric model, and systematically reduced this initial model to a one compartment model and further eliminated unidentifiabilities due to time scales. Kinetic analysis focuses on a time scale of seconds, thereby neglecting biosynthesis of new enzymes. We used linlog kinetics in representing the kinetic rate equations of each individual reaction. The final parameterization is performed for the final reduced model using previously published short term glucose perturbation data. The constructed model is a self-contained model in the sense that it can also predict the cofactor dynamics. Using the model, we calculated the Metabolic Control Analysis (MCA) parameters and found that the interplay among the growth, product formation and production of storage materials is strongly governed by the energy budget in the cell, which is in agreement with the previous findings. The model predictions and experimental observations agree reasonably well for most of the metabolites.

Appendix

Nomenclature Used for Metabolites in the Model

Below is the nomenclature list for metabolites used in the model, following the names in van Gulik et al. [29]

13PG

1,3-Bisphosphoglycerate

glc

Glucose

2PG

2-Phosphoglycerate

gln

Glutamine

3PG

3-Phosphoglycerate

glu

Glutamate

6APA

6-Aminopenicillinic acid

gly

Glycine

6Pgluct

6-Phosphogluconate

GMP

Guanosine monophosphate

8HPA

8-Hydroxypenillic acid

H

Proton

aAd

a-Aminoadipate

H2O

Water

AApool

Pool of free amino acids

H2S

Hydrogen sulfide

AAprotsyn

Amino acids for protein synthesis

HCoA

Coenzyme A

Ac

Acetate

his

Histidine

AcCoA

Acetyl coenzyme A

homcys

Homocysteine

AcHomser

o-Acetylhomoserine

homser

Homoserine

ACV

d-(a-Aminoadipyl)-cysteinylvaline

iCitr

Isocitrate

ADP

Adenosine-5-diphosphate

ile

Isoleucine

aKG

a-Ketoglutarate

IMP

Inosine monophosphate

aKI

a-Ketoisovalerate

ino

Inositol

ala

Alanine

iPN

Isopenicilline

AMP

Adenosine-5-monophosphate

lano

Lanosterol

arg

Arginine

leu

Leucine

asn

Asparagine

linCoA

Linoleoyl coenzyme A

asp

Aspartate

lys

Lysine

ATP

Adenosine-5-triphosphate

m1P

Mannitol-1-phosphate

bIM

b-Isopropylmalate

mal

Malate

biomass

Average biomass composition of glucose-limited cultures

man

Mannitol

carbP

Carbamoylphosphate

met

Methionine

CDPDAcgcl

Cytidine diphosphate-diacylglyerol

METHF

Methylene tetrahydrofolate

chit

Chitine

meva

Mevalonate

chor

Chorismate

MYTHF

Methyltetrahydrofolate

citr

Citrate

NAD

Nicotinamide adenine dinucleotide (oxidized)

CMP

Cytidine monophosphate

NADH

Nicotinamide adenine dinucleotide (reduced)

CO2

Carbon dioxide

NADP

Nicotinamide adenine dinucleotide phosphate

ctl

CTP

cys

E4P

Citruline

Cytidine triphosphate

Cysteine

Erythrose-4-phosphate

NADPH

Nicotinamide adenine dinucleotide phosphate

NH4

Ammonia

O2

Oxygen

OAA

Oxaloacetate

ergo

Ergosterol

OPC

6-Oxopiperidine-2-carboxylic acid

ery

Erythritol

PAA

Phenylacetic acid

ESE

Ergosterolester

PAACoA

Phenylacetyl coenzyme A

ExPept

Excreted peptides

PAPS

3-Phosphoadenosine-5-phosphosulfate

f16P

Fructose-1,6-bisphosphate

penG

Penicillin-G

f6P

Fructose-6-phosphate

PEP

Phosphoenolpyruvate

FAD

Flavine adenine dinucleotide (oxidized)

PHchol

Phosphatidylcholine

FADH2

Flavine adenine dinucleotide (reduced)

phe

Phenylalanine

FTHF

Formyltetrahydrofolate

PHeta

Phosphatidylethanolamine

fum

Fumarate

PHino

Phosphatidylinositol

g6P

Glucose-6-phosphate

phospht

Phosphatidate

GAP

3-Phosphoglyceraldehyde

PHser

Phosphatidylserine

gcl3P

3-Phosphoglycerol

Pi

Orthophosphate

pro

Proline

PROT

Protein

PRPP

a-5-Phosphoribosylpyrophosphate

psacch

Polysaccharides

pyr

Pyruvate

Rib5P

Ribose-5-phosphate

Ribu5P

Ribulose-5-phosphate

RNA

Ribose nucleic acid

SAM

S-Adenosylmethionine

sed7P

Sedoheptulose-7-phosphate

ser

Serine

succ

Succinate

succCoA

Succinyl coenzyme A

t6P

Trehalose-6-phosphate

THF

Tetrahydrofolate

thr

Threonine

tre

Trehalose

trp

Tryptophane

tyr

Tyrosine

UDP

Uridine-5-diphosphate

UDPglc

Uridine-5-diphosphoglucose

UMP

Uridine monophosphate

UTP

Uridine triphosphate

val

Valine

Xylu5P

Xylulose-5-phosphate

Data for the Kinetic Model

In the following, three tables are specified the finally used reactions, the input data, the assumed equilibrium constants and data on metabolite concentrations.

Table 8.15

Assumed equilibrium constants

Keq rxn

Value

Keq rxn

Value

r1.4

2.54510−6 M

r4.2

2.24106

r1.5

0.487

r4.3

0.041

r1.6

2.27103

r4.8

0.949

r1.7

0.0920

r4.9

0.85

r2.3

0.833

r4.11

2.4110−5 M

r2.4

1.82

r8.2

4.51010

r2.5

0.48

r11.1

9.8910−7

r2.6

0.37

r11.10

10.72

r2.7

0.0337

Table 8.16

Assumed metabolite concentrations

Metabolite

Assumed value

Pi:cyt

10 mM

NH4:cyt

0.1 mM

SO4:cyt

1 mM

H:cyt

10−7 M

arg:cyt

1 mM

P/O Ratio Calculations

The reactions describing the oxidative phosphorylation in [29] have to be updated/adjusted not only because the mitochondria compartment has been removed, but also, in [28], the experimentally determined P/O parameter was 1.84. The P/O parameter is changed in such a way to have the same theoretical yields for the reduced model as the original model. Using the Herbert-Pirt substrate utilization equation as a quality assessment to these reduction steps, we compared the Herbert-Pirt equation for the three compartment and the one compartment model.

We first considered the stoichiometric network presented in [29], which consists of 155 metabolites and 156 reactions located in three compartments (cytosol, mitochondria and peroxisome). The Herbert-Pirt substrate utilization relation can be written as:

$$ {q_S} = 5.17{q_{\rm{Pen}}} + 0.288\mu + 1.37\,{10^{{ - 3}}} $$

The P/O value is calculated from reaction r6.1 and r6.4. The first adjustment is to multiply the theoretical stoichiometric coefficients of mitochondrial and cytosolic protons, with the ratio of the estimated P/O ratio to the maximum P/O ratio

Subsequently the formation of ATP which is driven by the inward flux of cytosolic protons into the mitochondria (r6.4) is lumped with the water transport and the ADP/ATP shuttle (r10.3 and r10.1 respectively) in order to eliminate all mitochondrial reactants with exception of Hm.

Since the model does not contain any inner compartments, reactions l6.5 and l6.6 are parallel to each other, and are therefore lumped by averaging based on their steady state flux distribution (70.5–29.5% respectively). This yields the following lumped reaction:

This shows that the P/O ratio in the simplified model became 1.623 mol ATP/mol O. It should be noted that, the remaining ATP-balance parameters i.e. Kx, KPenG, mATP are kept unchanged in considering black-box balances

After modifying the model, we calculated the substrate Herbert-Pirt equation for the one compartment model.

We conclude that the obtained Herbert Pirt relation for the one compartment model is in agreement with the one for the three compartment model given the standard deviation in the ATP stoichiometry parameters.

Additional Details on the Identifiable Elasticities

List of identifiable elasticities as a function of the original parameters